Let #L1# be the perpendicular bisector and #L2# be the bisected line, as shown in the figure.

Given that the equation of the bisector #L1# is #8y+5x=4#,

#=> y=-5/8x+1/2#

Let #m_1# be the slope of #L1#, and #m_2# the slope of #L2#,

#=> m_1=-5/8#

Recall that the product of the slopes of two perpendicular lines is #-1#,

#=> m_2xxm_1=-1, => m_2=8/5#

#=># equation of #L2# is : #y-7=8/5(x-2)#

#=> y=8/5x+(19)/5#

Set the equations of #L1 and L2# equal to each other to find the intersection point #P(x_m, y_m)#, which is also the midpoint of #L2#.

#=> -5/8x+1/2=8/5x+19/5#

#=> x=-(132)/(89)#

#=> y=-5/8x+1/2=-5/8xx(-(132)/(89))+1/2=(127)/(89)#

#=> P(x_m,y_m)=(-(132)/(89), (127)/(89))#

Let the other end point of #L2# be #B(x,y)#,

Since #P# is the midpoint of #L2#,

#=> ((x+2)/2, (y+7)/2) = (-(132)/(89), (127)/(89))#

#=> (x,y)=(-(442)/(89), -(369)/(89))#